Answer:
a) The probability that a randomly selected adult consumes both cofee and soda is 0.3
b) the probability that a randomly selected adult doesnt consume at least one of cofee and soda is 0.7
c) The probability that a randomly selected adult consumes cofee but not soda is 0.25
Step-by-step explanation:
Lets pick a random adult and use the random variables
C = the adult consumes cofee
S = the adult consumes sodaa
we have that
P(C) = 0.55
P(S) = 0.45
P(C U S) = 0.7
a) We know that
0.7 = P(C U S) = P(C) + P(S) - P(C ∩ S) = 0.55 + 0.45 - P(C ∩ S)
Therefore
P(C ∩ S) = 0.55+0.45-0.7 = 0.3.
and as a consecuence, the probability that a randomly selected adult consumes both cofee and soda is 0.3.
b) The event 'a randomly selected adult doesnt consume at least one of the 2 products' is the complementary event of 'the adult consumes both cofee and soda', thus, the probability of this event is 1-P(C ∩ S) = 1 - 0.3 = 0.7.
c) Remember that
0.55 = P(C) = P(C ∩S) + P(C ∩ S^c) = 0.3 + P(C ∩ S^c)
Where S^c means that the adult doesnt consume soda. We can conclude that
P(C ∩ S^c) = 0.55-0.3 = 0.25
The probability that a randomly selected adult consumes cofee but not soda is 0.25.
